# Surface area + expression of a variable from formula - examples

- Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - 3rd dimension

The block has a surface of 42 dm^{2}and its dimensions are 3 dm and 2 dm. What is the third dimension? - Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm^{2}, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Tereza

The cube has area of base 256 mm^{2}. Calculate the edge length, volume and area of its surface. - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - Sphere A2V

Surface of the sphere is 241 mm^{2}. What is its volume? - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm^{3}. Calculate the surface area of the cylinder. - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3}. Calculate the volume, surface and diameter of the sphere. - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2}. Calculate the deviation of the side of this cone from the plane of the base. - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3}. What is it content (surface area)? - Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm^{3}. Calculate the surface of the prism. - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2}. - Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. - Airplane

Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies? - 3sides prism

The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism. - Cube wall

Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.

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